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In the single-processor scheduling problem with time restrictions there is one main processor and B resources that are used to execute the jobs. A perfect schedule has no idle times or gaps on the main processor and the makespan is therefore equal to the sum of the processing times. In general, more resources result in smaller makespans, and as it is in practical applications often more economic not to mobilize resources that will be unnecessary and expensive, we investigate in this paper the problem to find the smallest number B of resources that make a perfect schedule possible. We show that the decision version of this problem is NP-complete, derive new structural properties of perfect schedules, and we describe a Mixed Integer Linear Programming (MIP) formulation to solve the problem. A large number of computational tests show that (for our randomly chosen problem instances) only B=3 or B=4 resources are sufficient for a perfect schedule.
The purpose of this article is to evaluate optimal expected utility risk measures (OEU) in a risk-constrained portfolio optimization context where the expected portfolio return is maximized. We compare the portfolio optimization with OEU constraint to a portfolio selection model using value at risk as constraint. The former is a coherent risk measure for utility functions with constant relative risk aversion and allows individual specifications to the investor’s risk attitude and time preference. In a case study with three indices, we investigate how these theoretical differences influence the performance of the portfolio selection strategies. A copula approach with univariate ARMA-GARCH models is used in a rolling forecast to simulate monthly future returns and calculate the derived measures for the optimization. The results of this study illustrate that both optimization strategies perform considerably better than an equally weighted portfolio and a buy and hold portfolio. Moreover, our results illustrate that portfolio optimization with OEU constraint experiences individualized effects, e.g., less risk-averse investors lose more portfolio value in the financial crises but outperform their more risk-averse counterparts in bull markets.
Most of the land reforms of recent decades have followed an approach of “formalization and capitalization” of individual land titles (de Soto 2000). However, within the privatization agenda, benefits of unimproved land (such as land rents and value capture) are reaped privately by well-organized actors, whereas the costs of valorization (e.g., infrastructure) or opportunity costs of land use changes are shifted onto poorly organized groups. Consequences of capitalization and formalization include rent seeking and land grabbing. In developing countries, formal law often transpires to work in favor of the winners of the titling process and is opposed by the customary rights of the losers. This causes a lack of general acknowledgement of formalized law (which is made responsible for deprivation of livelihoods of vulnerable groups) and often leads to a clash of formal and customary norms. Countries may fall into a state of de facto anarchy and “de facto open access”. Encroachment and destruction of natural resources may spread. A reframing of development policy is necessary in order to fight these aberrations. Examples and evidence are provided from Cambodia, which has many features in common with other countries in Asia and Sub-Saharan Africa in this respect.